PIRSA:18090053

Towards a categorification of a projection from the affine to the finite Hecke algebra in type A

Tolmachov, K. (2018). Towards a categorification of a projection from the affine to the finite Hecke algebra in type A. Perimeter Institute. https://pirsa.org/18090053

Tolmachov, Kostiantyn. Towards a categorification of a projection from the affine to the finite Hecke algebra in type A. Perimeter Institute, Sep. 24, 2018, https://pirsa.org/18090053 

          @misc{ pirsa_PIRSA:18090053,
            doi = {10.48660/18090053},
            url = {https://pirsa.org/18090053},
            author = {Tolmachov, Kostiantyn},
            keywords = {Mathematical physics},
            language = {en},
            title = {Towards a categorification of a projection from the affine to the finite Hecke algebra in type A},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {sep},
            note = {PIRSA:18090053 see, \url{https://pirsa.org}}
          }

Kostiantyn Tolmachov

Talk number
PIRSA:18090053
Collection
Talk Type
Subject
Abstract

Work of Bezrukavnikov on local geometric Langlands correspondence and works of Gorsky, Neguţ, Rasmussen and Oblomkov, Rozansky on knot homology and matrix factorizations suggest that there should be a categorical version of a certain natural homomorphism from the affine Hecke algebra to the finite Hecke algebra in type A, sending basis lattice elements on the affine side to Jucys-Murphy elements on the finite side. I will try to explain some of the structures involved and will talk about recent progress towards a construction of such a categorification in the setting of Hecke categories.